Energy and Power

Let us consider an element in an electrical circuit through which a current I is flowing. Suppose there is a potential difference V across this element, and in a time $\Delta$t a charge $\Delta$Q passes by. The work $\Delta$W done by the electric field in moving this charge is given by, $\Delta$W = V$\Delta$Q . Thus, the work done per unit time, or the power P, is

 

$${\frac{\Delta W}{\Delta t}} {\frac{\Delta Q}{\Delta t}}$$ (5)

We recall the units of power are J/s, or Watts (W).

Electrical utilities normally bill on the basis of kilowatt-hours (kWh), which is the amount of energy the consumer has used in a given time period. One can convert kWh to J by the following formula:

$${\frac{{\:\rm J}\cdot\,{\:\rm h}}{{\:\rm s}}} {\frac{{\:\rm J}\cdot\,{\:\rm h}}{{\:\rm s}}}$$ (6)